Asymptotics of Sum of Heavy-tailed Risks with Copulas

TL;DR

This paper investigates the tail behavior of the sum of two heavy-tailed risks linked by copulas with tail order, providing asymptotic expansions for Value-at-Risk in various dependence scenarios.

Contribution

It introduces a method to analyze tail asymptotics of sums of heavy-tailed risks with copula dependence, including explicit asymptotic formulas for risk measures.

Findings

Derived asymptotic expansions for Value-at-Risk

Illustrated approach with multiple copula examples

Enhanced understanding of risk aggregation in heavy-tailed models

Abstract

We study the tail asymptotics of the sum of two heavy-tailed random variables. The dependence structure is modeled by copulas with the so-called tail order property. Examples are presented to illustrate the approach. Further for each example we apply the main results to obtain the asymptotic expansions for Value-at-Risk of aggregate risk.